Decision Theory

Decision Theory Part One: I tend to be risk-neutral, as much as possible, but like most people I can be a little bit risk averse. The situations in which I am most risk averse are those when taking the risk does not have a payoff that makes the risk worthwhile. This is probably closest to the minimax approach. For me, risk is very much situational. There are a few variables that I take into consideration. The first is information.

How much information I have will govern the amount of risk I'm willing to take in a situation. Even where I have strong motivation to take a risk, I feel that if I don't know enough, that I should be conservative. If the risk involves something with which I'm quite knowledgeable, I am far more likely to take the risk. The second variable is how extreme the risk is – the upside or the downside.

For example, while mathematically it makes no sense to play the lottery, the occasional ticket for a big draw has enough upside to accept that I'm probably lighting my money on fire. On the downside, there are some things where the downside risk, however minimal, is pretty severe.

So while there is little risk in jaywalking, the idea that should something bad happen it would probably involve me going to hospital, I just don't see why I would take that risk, when I could cross in a safer manner just a bit further down the road. That said, I'm more likely to jaywalk in a place I frequent than some other city where maybe I don't know the traffic patterns.

Taking these variables into account, my risk-taking behavior is still fairly risk neutral or slightly risk averse, but there are certain variables that could influence my decision in a way that convinces me to take more risk, every now and again. In a public sector situation, I would probably always be risk averse. Given the complexity of decisions, I would know that there are things I do not know.

Furthermore, if my decisions are going to affect other people, I will probably take a more risk averse approach, maybe even shift towards a maximin approach. For example, making a decision to invest taxpayer dollars in, say, a decision to upgrade police equipment. I would look at the downside, for example if I decline and some crime happens that the equipment could have helped prevent. That downside would drive my decision-making, because of how it affects other people.

Thus professional decision-making is a bit different, and definitely more risk averse than personal risk taking. That is part of being a public servant, to steward the public's resources in a safe and responsible manner. For me, that usually means minimizing the downside risk associated with my decisions. The police scenario is one where human life is at play, and as such that creates a specific obligation on my part, I feel, that influences the criteria by which I evaluate decisions.

Part Two: For any decision, there are a number of possible outcomes, which is where decision trees and sensitivity analysis come into play. Building on the example of a decision to upgrade police equipment, we can look at the potential variables. The cost is a certainty, but the outcomes are not.

They might be a) new equipment prevents crime, but we might not know that this has happened; b) no new equipment and the crime occurs; c) no new equipment and no crime occurs or d) new equipment, but the crime occurs anyway. Two of those are positive outcomes, one coming with the cost and one without. Two of those are negative outcomes, one with the cost and one without. The decision tree approach would take the odds of each event occurring.

If your data suggests that the expensive equipment will not prevent the crime anyway, you might decision not to bother with the equipment. If data suggests that the crime is highly unlikely regardless, you would not spend the money. Only where the purchase-do not purchase decision influences the likelihood of the crime occurring would you then make a decision on that basis. Understanding the odds of each scenario is important when using a decision tree. The sensitivity analysis technique can be applied in another way as well.

The odds of an outcome can be distilled to an expected outcome. This is how it works when the question is financial, or quantitative in nature. Sensitivity analysis allows you to see what might happen under a number of different scenarios. If you are giving a tax break to an industry, that is a cost to the taxpayer, and can be quantified. The benefits, however, are unknown. If that industry creates 10 jobs, or 100 jobs, or 1000 jobs, each will have different outcomes.

The decision-maker can understand what the outcome will be under each scenario using sensitivity analysis.